The problem arose because we make extensive use of template override files - a great way of changing the way a page looks without hacking the core of components, but in the case where core elements of the component are changed (such as in the upgrade to K2 2.5.x) the template overrides need to be updated too!
Updating template overrides is pretty easy if you know what part of the file you need to update, and what you need to replace it with. In this case we need to edit the item.php file, which controls how the individual item pages are displayed. This can be found in templates>yourtemplate>html>com_k2>templates>yourtemplatename.
What needed to be done was changing the attachments block to reflect the new way of managing attachements, as below:
<span><?php echo JText::_('K2_DOWNLOAD_ATTACHMENTS'); ?></span>
<?php foreach ($this->item->attachments as $attachment): ?>
<a title="<?php echo htmlentities($attachment->titleAttribute, ENT_QUOTES, 'UTF-8'); ?>" href="/<?php echo $attachment->link; ?>">
<?php echo $attachment->title ; ?>
<?php if($this->item->params->get('itemAttachmentsCounter')): ?>
<span>(<?php echo $attachment->hits; ?> <?php echo (count($attachment->hits)==1) ? JText::_('K2_DOWNLOAD') : JText::_('K2_DOWNLOADS'); ?>)</span>
<?php endif; ?>
<?php endforeach; ?>